// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

/* This file is a modified version of heap_relax_snode.c file in SuperLU
 * -- SuperLU routine (version 3.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * October 15, 2003
 *
 * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.
 *
 * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
 * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.
 *
 * Permission is hereby granted to use or copy this program for any
 * purpose, provided the above notices are retained on all copies.
 * Permission to modify the code and to distribute modified code is
 * granted, provided the above notices are retained, and a notice that
 * the code was modified is included with the above copyright notice.
 */

#ifndef SPARSELU_RELAX_SNODE_H
#define SPARSELU_RELAX_SNODE_H

namespace Eigen {

namespace internal {

    /** 
 * \brief Identify the initial relaxed supernodes
 * 
 * This routine is applied to a column elimination tree. 
 * It assumes that the matrix has been reordered according to the postorder of the etree
 * \param n  the number of columns
 * \param et elimination tree 
 * \param relax_columns Maximum number of columns allowed in a relaxed snode 
 * \param descendants Number of descendants of each node in the etree
 * \param relax_end last column in a supernode
 */
    template <typename Scalar, typename StorageIndex>
    void
    SparseLUImpl<Scalar, StorageIndex>::relax_snode(const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end)
    {
        // compute the number of descendants of each node in the etree
        Index parent;
        relax_end.setConstant(emptyIdxLU);
        descendants.setZero();
        for (Index j = 0; j < n; j++)
        {
            parent = et(j);
            if (parent != n)  // not the dummy root
                descendants(parent) += descendants(j) + 1;
        }
        // Identify the relaxed supernodes by postorder traversal of the etree
        Index snode_start;  // beginning of a snode
        for (Index j = 0; j < n;)
        {
            parent = et(j);
            snode_start = j;
            while (parent != n && descendants(parent) < relax_columns)
            {
                j = parent;
                parent = et(j);
            }
            // Found a supernode in postordered etree, j is the last column
            relax_end(snode_start) = StorageIndex(j);  // Record last column
            j++;
            // Search for a new leaf
            while (descendants(j) != 0 && j < n) j++;
        }  // End postorder traversal of the etree
    }

}  // end namespace internal

}  // end namespace Eigen
#endif
